With the increasing maturity of wireless communication, integrated circuit, sensor and micro electro mechanical system (MEMS), it is possible to produce micro wireless sensors with low cost, low power consumption and multi-function. These sensor nodes integrate functional components such as information sensing, data processing and wireless communication [1]. WSN is a wireless self-adjusting network composed of multiple miniature smart sensor nodes sent to the monitoring area. Its purpose is to monitor, perceive and collect the data of various environments or monitoring objects in the geographical area covered by the network in real time, process these data, obtain detailed and accurate information and transmit them to users who need these information. With the help of various sensor units built in the node, the signals of heat, infrared, magnetism, image, sonar, radar and seismic wave in the surrounding environment are measured, so as to detect many physical phenomena of interest, including temperature, humidity, noise, light intensity, pressure, soil composition, size, speed and direction of moving objects. WSN is usually deployed in extreme environments that cannot be reached or stationed for a long time, such as the field or disaster site. Widely used in national defense and military industry, anti-terrorism and disaster prevention, smart home, environmental protection, earthquake and extreme weather, risk control, vehicle control, medical maintenance, manufacturing and other fields. This is currently very active research. Cai M et al. regard wireless sensor networks as a new technology for information understanding, detection and processing. If the Internet recognizes that the world communicates for digital purposes and changes the way people communicate; then, WSN recognizes the connection between the digital world and the physical goals of the world, changes the interaction of people and events, and marks the coming of counting time[2]. Zhang J and others found that WSN originated from the combat needs of the U.S. military. Since the mid-1990s, WSN has attracted great attention from the military, academia and industry. The United States has invested heavily in supporting the research of WSN through the Advanced Research Projects Agency (DARPA) of the Ministry of defense and the National Natural Science Foundation (NSF) [3]. Typical research projects include DARPA's SensIT(Sensor Information Technology) research plan, which includes 29 research projects. At present, some sensor nodes and operating systems that can be put into practical use have been developed. Representative sensor nodes are mica series and Imote2 series produced by crossbow company. Ti, Freescale and other companies have developed ZigBee series chips such as CC2430. Famous operating systems include TinyOs developed by UCB and SOS developed by UCLA, but SOS has not been upgraded since 2008. In recent years, the National Natural Science Foundation of China, 863 program and 973 program have provided large-scale and high-intensity research funding in the field of WSN, which has accelerated the research process of WSN in China. In China, the earlier institutions to carry out WSN related research include Institute of computing, Institute of software, Chinese Academy of Sciences, Harbin Institute of technology, Tsinghua University, Shanghai Jiaotong University, Peking University, Nanjing University, National Defense University, Zhejiang University, Fudan University, Beijing University of Posts and telecommunications, Central South University, Hunan University, etc. At the beginning of 2006, 973 Plan established the basic theory and key technology research project of wireless sensor networks. More than ten key universities, including Hong Kong University of science and technology and Shanghai Jiaotong University, jointly carried out research on all levels of sensor networks. Ningbo Zhongke integrated circuit design center (NBICC) was established by the Institute of computing of the Chinese Academy of Sciences in cooperation with Ningbo municipal government. It specializes in providing solutions and system integration based on radio frequency identification system (RFID), wireless network and electronic tag equipment. Ningbo high tech Zone Shenlian Technology Co., Ltd. is a high-tech enterprise incubated by NBCC wireless communication division, specializing in short-range wireless communication such as WSN and RFID, embedded communication solutions, etc. Shenlian technology has been engaged in the research and development of wireless communication, embedded, especially WSN. It is a leader in the industrialization of WSN in China. Its gain series nodes and development kits have a high market share in China. The Chinese government has always attached importance to the development of sensor networks. The outline of the national medium and long term science and technology development plan released in early 2006 identified three cutting-edge directions for information technology, two of which are directly related to WSN research. In November 2008, IBM proposed “smart earth”, whose core view is to integrate the Internet of things and the Internet to realize the integration of human society and the physical world. Chen Jie and others believe that the so-called Internet of Things refers to a large-scale network integrated with various data measurement devices, such as RFID, infrared sensors, earthmoving systems, laser scanners, and other devices connected to the Internet or telephone communication[4]. Put sensors on everything that has nothing to do with the network but is closely related to our life and work, and then connect with the existing network, so that people can identify, control and manage these things more directly through computers or mobile phones. In August 2009, Premier Wen Jiabao of the State Council said during his visit to Wuxi Gaoxin micro nano sensor network engineering technology research and development center of the Chinese Academy of Sciences that at least three things can be done as soon as possible: first, combine the sensor system with TD technology in 3G; Second, accelerate the development of sensor networks in major national science and technology projects; Third, establish China's sensing information center, or “sensing China” center, as soon as possible. In September 2009, the National Information Technology Standardization Technical Committee established the working group on sensor network standards, which means that China's “Internet of things” standard has been preliminarily established. One of the main tasks of wireless sensor networks is to collect data in the monitoring area. Sensor nodes have limited energy, bandwidth, computing and storage capacity. How to achieve low energy consumption and high security data collection in resource constrained and node intensive WSN is an important problem that researchers need to solve. Because sensor nodes usually have a certain data processing capacity, they can process the original sensor data in the network through the cooperation between sensor nodes, and then transmit the processing results to sink nodes, so as to save data transmission energy consumption, reduce bandwidth requirements and improve the efficiency of data collection. At the same time, in the process of data transmission, security issues such as data confidentiality, source authentication, integrity and freshness should be considered [5]. Aiming at energy, delay, security and storage efficiency, this paper focuses on the data collection in wireless sensor networks, focusing on the data compression algorithm and data authentication mechanism in the process of data collection from sensor collection site to sink.

Wireless sensor networks consist of many affordable tiny sensors. It creates personal organization through wireless multi-hop communication. It understands, compiles and records the information found within the coverage area and sends it to the inspector. Network architecture of wireless sensor networks [6]. Sensing object, sensor and observer constitute the three elements of sensor network. In addition to information collection and data processing, each node in the network also undertakes the storage, management and integration of forwarded data. At the same time, it has the dual functions of terminal and routing. At present, the software and hardware technology of sensor nodes is the research focus of sensor networks. Wireless sensor networks are composed of sensor nodes distributed in specific areas, which are used to monitor specific objects such as temperature, humidity, vibration and so on. A single node in wireless sensor networks is generally composed of sensor module, microprocessor module, wireless communication module and energy supply module.

Although the sensor nodes in the network accomplish special data and network communication, there are still some limitations and limitations.

In order to meet the portable and mobile application requirements of sensor nodes, nodes are generally powered by batteries with very limited energy. Sensor nodes are usually delivered randomly, the deployment area environment is complex, and even some area personnel cannot reach, so it is difficult to supplement energy by battery replacement [7]. Therefore, energy is an extremely important and limited resource in wireless sensor networks, and it is also the main constraint of nodes.

The energy consumption of sensor nodes mainly comes from microprocessor module, sensor module and wireless communication module. With the progress of integration technology and microelectronics technology, the energy consumption of microprocessor and sensor is getting lower and lower, so that the wireless data communication part consumes most of the energy of the system. The energy consumption of sensor nodes is as follows. Facing the huge communication cost, how to reduce the amount of communication data has become the key to reduce energy consumption.

Nodes in wireless sensor networks are usually low-cost and low-power micro embedded devices, and the processor capacity and memory capacity will be limited. On the other hand, due to the limitation of energy, nodes cannot use high-performance and high-power processors. How to use limited computing and storage resources to complete specific tasks has become a challenge in the process of node software design.

The distance of wireless communication is the most important factor to determine the communication energy consumption. In addition, the mirror reflection of obstacles, antenna quality and other factors will also affect the communication distance, and the energy consumption of nodes will increase significantly with the increase of wireless communication distance. In order to reduce energy consumption, the communication distance should be minimized on the premise of meeting the connectivity requirements. On the other hand, the communication bandwidth of sensor nodes is also very limited, usually only a few hundred Kbps. From the above limitations faced by sensor nodes, it can be seen that energy limitation is the main limitation, and other limitations also come from the limitation or correlation of energy. How to use limited energy and limited bandwidth to complete the transmission of a large amount of data under the condition of limited computing and storage resources, reduce the energy consumption of nodes and prolong the life cycle of equipment will be the biggest challenge faced by wireless sensor networks [8].

Given that the communication power consumption of sensor nodes is higher than that of processors, reducing the cost of data communication will be an important way to reduce system power consumption. Among them, data compression is one of the very effective methods, which has become the research hotspot of energy-saving methods in wireless sensor networks. Because the node monitoring data usually changes slowly in a short time, the data may be relevant in time; Nodes are densely deployed in the monitoring area, and multi-point cooperation may be adopted, so that the data perceived by adjacent nodes may also be spatially relevant. In addition to the temporal and spatial correlation, the monitoring data may also show certain temporal and spatial regularity, such as certain trend, distribution characteristics or repeatability. These temporal and spatial correlation and regularity of the data provide the possibility for data compression. Compared with the emerging wireless sensor networks, data compression technology, as an important research field in Information Science, has a long history of development [9]. The combination of data compression technology and wireless sensor network to reduce the amount of communication data not only reduces the energy consumption of nodes, but also effectively reduces the network congestion. For the whole network, it improves the data transmission efficiency and bandwidth utilization, and reduces the energy consumption of the whole network, as shown in Table 1.

Classification of resource constraints of hardware platform

Platform | Power supply | Storage space | Processing capacity |
---|---|---|---|

personal computer | infinite | Unrestricted | Unrestricted |

High end embedded | Limited | Relatively limited | Relatively limited |

Low end embedded | Extremely limited | Extremely limited | Extremely limited |

The resources of the hardware platform determine the scale of the running algorithm. According to the different constraints of the hardware platform resources (energy supply, storage space and processing capacity), the application platforms of the current algorithm can be divided into several categories as shown in Table 1. For general wireless sensor network nodes, not only the power supply is extremely limited, but also the storage space and processing capacity are limited. However, traditional data compression algorithms usually run on personal computers with almost unlimited resources, and take the compression rate as the measurement standard of the algorithm. When these compression algorithms are introduced into wireless sensor networks, while pursuing high compression rate to reduce communication energy consumption, we must also consider the resource constraints of WSN, and take the energy-saving benefit of the algorithm as the measurement standard. Therefore, this also puts forward new requirements for the compression algorithm.

Energy saving is the most important purpose of applying data compression technology to wireless sensor networks, that is, reducing the energy consumption of nodes by reducing the amount of communication data. At the same time, the operation of compression algorithm on hardware increases the energy consumption of nodes. Therefore, in order to ensure that the running compression algorithm can bring a certain energy-saving effect to the node, it must be required that the energy consumed by running the compression algorithm should be less than the transmission energy of sending the reduced amount of data through compression, otherwise the significance of data compression will be lost.

As can be seen from table 1, in addition to the limited energy, the calculation and processing capacity of sensor nodes is also limited, which is mainly reflected in the storage space and processing capacity. Therefore, it can not bear or realize a large number of complex operations. The limited computing capacity of node microprocessor requires that the time complexity of the algorithm should be as low as possible; The storage medium with limited nodes requires that the amount of dynamic data of the algorithm cannot be too much. For example, K-L transform, nonlinear prediction, subband coding and so on will not be directly introduced into the sensor node.

The compression algorithm running on the sensor node finally needs the source program to realize. The low time complexity of the compression algorithm itself is the premise of efficient algorithm execution. However, due to the subjectivity of the algorithm source program in the programming process, there will be some differences in the execution efficiency of the algorithm source program realized by different implementation methods [10]. Therefore, in addition to considering the complexity of the algorithm, the data compression algorithm in wireless sensor networks also needs to consider the efficiency of the algorithm itself. Appropriate optimization methods should be introduced in the process of source program design to improve the execution efficiency of the algorithm.

The design of data compression algorithm usually aims at specific data objects, that is, the algorithm can obtain good compression effect under a specific data condition. For example, LZW is suitable for text data compression, run length coding is suitable for compressing a large number of continuous character data, etc. When the data characteristics change, the compression effect will change significantly. The environment detected by sensor nodes is usually unknown and the data characteristics are unstable. In order to obtain good compression effect, the algorithm should have fixed dynamic characteristics and be able to dynamically adapt to the changes of environment and data characteristics.

For the traditional applications of data compression, compression algorithms mainly focus on using data compression technology to reduce the amount of data, so as to effectively reduce the storage space of data, reduce the time and transmission bandwidth of data communication. When these algorithms are improved and introduced into wireless sensor networks, some original evaluation indexes of algorithms are also introduced. At present, several common indicators for evaluating the performance of compression algorithms are as follows:

The data collected by sensor nodes can be described as a matrix structure, as shown in formula (1) where the row vector represents a single parameter to sample the dataset over the time series. The

For strongly correlated parameters (such as air temperature and soil temperature), a standard linear regression estimation model is used to establish a mathematical relationship equation between the parameters, as shown in (2), and the least squares method is used to determine the fitting equation when the fitting error RMSE is the smallest. Regression coefficients (a, b). The sensor network node sends Y; as the reference data set BD (Base Data) to the base station, and the transmission of the Y; data set can be realized by only sending the regression coefficients (a, b) of the fitting equation, see equation (2).

However, performing linear regression on the entire time series will produce relatively large errors, mainly due to: (1) The correlation degree of parameters in different time periods is different. For example, the rate of change of ambient temperature is small in the noon time of the day, while the rate of change is large in the evening. ② The interaction of different parameters has a lag in the time dimension. When a parameter changes, the corresponding changes in other related parameters are delayed. For example, the interaction between ambient temperature and soil temperature. A piecewise linear regression mapping method is proposed, which divides the sample data on the time series into segments, performs linear regression calculation in units of segments, and performs feature description in the form of a self-defined structured reduced set S, as defined in Definition 1. After the _{j}_{j}_{j}_{i}_{i}

Assuming that the data representation of the sensor acquisition parameters and the data representation of the S-member parameters of the structured and reduced set occupy the same storage space, the data compression rate can be simplified as shown in Equation (4):

In the formula: _{i}

Algorithm complexity

The complexity of an algorithm is an important index to reflect the quality of an algorithm. In data compression algorithms, algorithm complexity actually refers to the hardware resources required in the compression process, usually including the time complexity and space complexity of the algorithm, that is, the amount of computation and storage required by the algorithm. Time complexity refers to the relationship between time frequency

In the process of evaluating the energy efficiency of data compression, in order to make the analysis not stick to the specific environment and specific algorithm, the hardware factors and algorithm factors are discussed separately. The characteristics of typical sensor nodes' hardware environment and typical data compression algorithm are shown in Table 2 respectively.

Hardware structure of typical sensors

Node platform | Organization / manufacturer | Microprocessor | RF chip |
---|---|---|---|

Mica2 | UCB | AT mega128L | CC1000 |

Micaz | UCB | AT mega128L | CC2420 |

Toles | UCB | TI MSP430F149 | CC2420 |

T-mote sky | Moteiv | TI MSP430F2611 | CC2420 |

ZebraNET | Princeton | TI MSP430F149 | 9XStream |

EyesIFX | EURO | TI MSP430F149 | TDA5250 |

TinyNode | TinyNode | TI MSP430F2618 | XE1205 |

Fleck3 | SCIRO | AT mega128L | nRF905 |

Imote2 | Intel | Intel PXA271 XScale | CC2420 |

u AMPS-I | MIT | SA1100 | LMX3162 |

It can be seen from Table 2 that the microprocessors used on typical sensor nodes mainly include ATmegl28L, MSP430 series, PXA271, SA11000, etc. their average current consumption under different working environments is shown in Table 3:

Operating characteristics and average current of common microprocessors on sensor nodes

Microprocessor | Working voltage | Operating frequency | Average current consumption |
---|---|---|---|

ATmega128 | 2.7V | 1MHz | 1.9mA |

3.3V | 1MHz | 2.1mA | |

2.7V | 8MHz | 7.5mA | |

3.3V | 8MHz | 9. 5mA | |

MSP430F2611 |
2.2V | 4KHz | 2.1uA |

3.0V | 4KHz | 3.0uA | |

2.2V | 1MHz | 365uA | |

3.0V | 1MHz | 512uA | |

MSP430F149 | 2.2V | 4KHz | 2.5uA |

3.0V | 4KHz | 9.0uA | |

2.2V | 1KHz | 280uA | |

3.0V | 1KHz | 420uA | |

ML67Q5002 | 2.5V | 60MHz | 75mA |

The efficiency and low complexity of the software algorithm itself is the key to reduce the system energy consumption, but under the premise of the same algorithm, the efficiency of the algorithm implementation process source program is also very important [12]. High level language not only simplifies the development process of the algorithm, but also reduces the efficiency of program execution. At the same time, it makes the coding efficiency of different programmers different. Therefore, there is a lot of room for improvement in the optimization of software energy consumption at the source program level. In addition, for current microprocessors, there is a common feature, that is, the capacity of program memory is often much larger than that of data memory, and there are few internal registers. Although the microprocessor is also improving in hardware and the capacity of program memory is increasing, the capacity of data memory (RAM) and the number of internal registers change very little. This resource is relatively short, which also makes it possible to optimize the source program. As the most widely used high-level language, C language has high operation efficiency and good portability, and is often used in the development of underlying programs of embedded systems [13]. Wireless sensor network node is a low-end embedded hardware platform, and C language is the most commonly used development language. Therefore, the research on the algorithm source program level energy consumption optimization method of C language is of great significance to reduce the system operation energy consumption. The program is composed of data structure and algorithm. Different data organization forms and data types will correspond to different access methods and data formats. Both of them determine the execution efficiency and corresponding energy consumption level of the program to a great extent. Adjusting the storage and distribution mode of data in the source program of data compression algorithm in wireless sensor networks is of great significance to reduce the energy consumption of the algorithm.

In C language, all statements are executed in the order of top-down. Even statements or expressions with the same status in structure have the order of execution. For example, the logical operation of each branch of the selection structure and multiple relational expressions, and the sequence of the selected branches and relational expressions do not affect the functions realized by the source program. When the probability distribution of the execution of these branches with the same status is uneven, or the probability of the establishment of the expression is different, the sequence of executing statements or expressions will affect the execution efficiency of the source program. Therefore, when these probabilities are known, adjusting the order of statements or expressions is conducive to improve the execution efficiency of the source program and reduce the system energy consumption. The adjustable range of the hardware coefficient of the sensor node is [111, 227], so the algorithm adjustment points within this adjustment range are only kwch-S- lz W. b-RLA, that is, only [S-LZW, b~RLE] algorithm combination meets the requirements. Through the above test, the algorithm combination for algorithm adjustment and the k value of adjustment point can be obtained. Applying the combination of this algorithm and the values of adjustment points to the lossless compression of node data can realize the data compression with power consumption perception, so that the energy efficiency of nodes can be dynamically maintained at a high level [14].

As an important energy-saving means, data compression is a research hotspot in wireless sensor networks. The research on data compression in wireless sensor networks mainly involves two problems: one is how to objectively and comprehensively evaluate the compression algorithm and establish the corresponding evaluation index; The second is how to improve the energy-saving effect of compression algorithm and prolong the life cycle of nodes. Since energy saving is the primary purpose of WSN data compression, in addition to the traditional evaluation indexes, the relevant evaluation standards should be energy related, focusing on the energy-saving effect of the algorithm; In addition, because the development process of data compression is much earlier than that of wireless sensor networks, and the algorithm has been relatively mature, there is little space to improve the performance of compression by improving the algorithm itself, so we need to rely on other auxiliary methods to further improve the performance of the algorithm. To solve the above problems, focusing on the energy efficiency of compression algorithm, this paper involves two main parts: energy efficiency evaluation index and energy efficiency improvement method. The innovations and contributions of this paper are as follows: Based on the existing energy efficiency evaluation indexes and the characteristics of wireless sensor networks, an improved scheme of energy efficiency evaluation is proposed. The scheme separates the hardware factors and algorithm factors in the original energy efficiency index, makes the evaluation process more flexible and more suitable for wireless sensor networks, simplifies the original evaluation index, and the new scheme is more conducive to the analysis of the influencing factors of energy efficiency.

#### Operating characteristics and average current of common microprocessors on sensor nodes

Microprocessor | Working voltage | Operating frequency | Average current consumption |
---|---|---|---|

ATmega128 | 2.7V | 1MHz | 1.9mA |

3.3V | 1MHz | 2.1mA | |

2.7V | 8MHz | 7.5mA | |

3.3V | 8MHz | 9. 5mA | |

MSP430F2611 |
2.2V | 4KHz | 2.1uA |

3.0V | 4KHz | 3.0uA | |

2.2V | 1MHz | 365uA | |

3.0V | 1MHz | 512uA | |

MSP430F149 | 2.2V | 4KHz | 2.5uA |

3.0V | 4KHz | 9.0uA | |

2.2V | 1KHz | 280uA | |

3.0V | 1KHz | 420uA | |

ML67Q5002 | 2.5V | 60MHz | 75mA |

#### Classification of resource constraints of hardware platform

Platform | Power supply | Storage space | Processing capacity |
---|---|---|---|

personal computer | infinite | Unrestricted | Unrestricted |

High end embedded | Limited | Relatively limited | Relatively limited |

Low end embedded | Extremely limited | Extremely limited | Extremely limited |

#### Hardware structure of typical sensors

Node platform | Organization / manufacturer | Microprocessor | RF chip |
---|---|---|---|

Mica2 | UCB | AT mega128L | CC1000 |

Micaz | UCB | AT mega128L | CC2420 |

Toles | UCB | TI MSP430F149 | CC2420 |

T-mote sky | Moteiv | TI MSP430F2611 | CC2420 |

ZebraNET | Princeton | TI MSP430F149 | 9XStream |

EyesIFX | EURO | TI MSP430F149 | TDA5250 |

TinyNode | TinyNode | TI MSP430F2618 | XE1205 |

Fleck3 | SCIRO | AT mega128L | nRF905 |

Imote2 | Intel | Intel PXA271 XScale | CC2420 |

u AMPS-I | MIT | SA1100 | LMX3162 |

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Research on innovative human capital for China’s economic development based on STI model In-depth analysis of the artistic expression of paper-cut elements in the design of boat space Knowledge graph construction and Internet of Things optimisation for power grid data knowledge extraction Modeling the pathway of breast cancer in the Middle East Construction and intelligent analysis of power grid physical data knowledge graph based on Internet of Things for power system Research on industrial Internet of Things and power grid technology application based on knowledge graph and data asset relationship model Research on the effects of financial literacy on rural household credit constraint Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on educational resource recommendation system based on MRLG Rec The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations A study on the phenomenon of anaphoric correction in college students’ English conversation Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Limit cycles of a generalised Mathieu differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model Design of fitness walker for the elderly based on ergonomic SAPAD model AtanK-A New SVM Kernel for Classification Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Design and evaluation of intelligent teaching system on basic movements in PE Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network